Solve Easy Vector Problem: Find Displacement of Clock Hands from 3pm-6pm

  • Thread starter Thread starter whizbang21
  • Start date Start date
  • Tags Tags
    Vector
AI Thread Summary
To find the displacements of the clock hands from 3 PM to 6 PM, the minute hand, which completes a full rotation every hour, will have a displacement of zero since it returns to the same position. The hour hand, however, moves from the 3 o'clock position to the 6 o'clock position, covering an angular displacement of 90 degrees. The Cartesian coordinates for the tip of the hour hand at 3 PM are (0.23, 0) and at 6 PM are (0, 0.23). The displacement vector for the hour hand can be calculated using the difference in coordinates, resulting in a displacement of (-0.23, 0.23). Understanding the definitions of displacement and vector quantities is crucial for solving this problem accurately.
whizbang21
Messages
6
Reaction score
0
1. A wall clock has a minute hand with a length of 0.45 m and an hour hand with a length of 0.23 m. Take the center of the clock as the origin, and use a Cartesian coordinate system with the positive x-axis pointing to 3 o'clock and the positive y-axis pointing to 12 o'clock. Find the displacements of the tip of each hand (that is, ΔAarrowbolditalic and ΔBarrowbolditalic) when the time advances from 3:00 P.M. to 6:00 P.M. (Aarrowbolditalic and Barrowbolditalic represent the tip of the hour hand and the tip of the minute hand, respectively.)

Let the +y direction be straight up and the +x direction be to the right. Recall the definition of displacement, and remember that positions are vector quantities.

Homework Equations


dont know, tried Pythagorean theorem.

The Attempt at a Solution


the part dealing with the minute hand is obviously 0. but as far as the hour hand, I've tried using the pythagorean theorem to calculate the displacement which would just be sqrt((.23^2)+(.23^2)^2) but apparently that was wrong, or maybe i just put the wrong sign. only have 1 more submission so not about to guess it.
 
Physics news on Phys.org
halp
 
can you calculate their angular displacements?
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top